Method of monitoring the pressure of an aircraft tire

ABSTRACT

A method of monitoring the pressure of a tire of an aircraft, the method including: taking two or more pressure readings from the tire at different times; calculating an estimated deflation rate based on the pressure readings; and calculating a time for the tire to deflate to a reference pressure level based on the estimated deflation rate. Two or more temperature readings are each associated with one of the pressure readings, and the estimated deflation rate is calculated by normalising each pressure reading based on its associated temperature reading and a common reference temperature to obtain a temperature-normalised pressure reading, and calculating the estimated deflation rate based on the temperature-normalised pressure readings. The estimated deflation rate is compared with a threshold, and a warning provided if the estimated deflation rate exceeds the threshold.

RELATED APPLICATION

The present application claims priority to GB Patent Application Number1504777.2, filed Mar. 20, 2015, the disclosure of which is entirelyincorporated by reference.

FIELD OF THE INVENTION

The present invention relates to a method of monitoring the pressure ofa tire of an aircraft, and apparatus for performing such a method.

BACKGROUND OF THE INVENTION

An aircraft tire monitoring system is disclosed in U.S. patentapplication publication 2008/0055060 A1. A sensor senses an operatingparameter of the tire (such as pressure or temperature), and a signalrelated to the sensed parameter is transmitted to a reader located on orin an aircraft fuselage. The reader may also transmit some or all of theinformation to another device, such as a display.

SUMMARY OF THE INVENTION

A first aspect of the invention provides a method of monitoring thepressure of a tire of an aircraft, the method comprising: taking two ormore pressure readings from the tire at different times; and calculatingan estimated deflation rate based on the pressure readings.

A second aspect of the invention provides an apparatus for monitoringthe pressure of a tire of an aircraft, the apparatus comprising: apressure sensor for taking pressure readings from the tire at differrent times; and a computer system configured to calculate an estimateddeflation rate based on two or more of the pressure readings.

Optionally a time for the tire to deflate to a reference pressure levelis estimated based on the estimated deflation rate. The estimated timecan then be stored for later analysis and/or displayed to flight ormaintenance crew to enable them to take appropriate action.

Optionally the estimated deflation rate is compared with a threshold,and a warning provided if the estimated deflation rate exceeds thethreshold.

If a temperature of the tire remains constant between the differentpressure readings, then they can be directly used to calculate theestimated deflation rate. More typically the method comprises for eachpressure reading taking an associated temperature reading, and theestimated deflation rate is calculated by normalising each pressurereading based on its associated temperature reading and a commonreference temperature to obtain a temperature-normalised pressurereading, and calculating the estimated deflation rate based on thetemperature-normalised pressure readings. The temperature readings maybe taken by a temperature sensor carried by a wheel on which the tire ismounted, for example, or by a temperature sensor in any other suitablelocation (for instance a brake temperature sensor, or an ambienttemperature sensor). The temperature readings may be taken at the sametime as their associated pressure readings, or shortly before or aftertheir associated pressure readings.

The pressure readings may all be taken with the aircraft on the ground,or at least one of the pressure readings may be an in-flight pressurereading taken from the tire when the aircraft is in flight.

Typically at least one of the pressure readings is an in-flight pressurereading taken from the tire when the aircraft is in flight with the tireunloaded, and the estimated deflation rate is calculated by adjustingthe in-flight pressure reading to take account of the tire beingunloaded to obtain a load-adjusted in-flight pressure reading, andcalculating the estimated deflation rate based on the load-adjustedin-flight pressure reading.

Optionally the in-flight pressure reading is normalised based on itsassociated temperature reading and the common reference temperature andalso adjusted to take account of the tire being unloaded, to obtain atemperature-normalised and load-adjusted in-flight pressure reading, andthe estimated deflation rate is calculated based on thetemperature-normalised and load-adjusted in-flight pressure reading.

The estimated deflation rate may be calculated based on only twopressure readings, but more typically it is calculated based on three ormore pressure readings taken from the tire at different times. Typicallythe estimate deflation rate is calculated by fitting a curve or straightline to the pressure readings, for instance by a least-squares fittingalgorithm

Optionally first and second times are estimated for the tire to deflateto first and second reference pressure levels (for instance 100% and 95%of a nominal reference pressure). Optionally the first and second timesare displayed at the same time on a single display device.

Optionally the time for the tire to deflate to the reference pressurelevel is calculated by reducing a selected one of the pressure readingswith respect to a lower temperature to obtain a temperature-adjustedpressure level, and calculating a time for the tire to deflate from thetemperature-adjusted pressure level to the reference pressure levelbased on the estimated deflation rate.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described with reference to theaccompanying drawings, in which:

FIG. 1 is a plan view of an aircraft;

FIG. 2 shows one of the landing gears of the aircraft and its associatedsensor systems;

FIG. 3 shows two of the sensor systems connected to a cockpit computersystem;

FIG. 4 shows some of the elements of the cockpit computer system;

FIG. 5 is a graph showing eight pressure readings; and

FIG. 6 is an example of a screen displayed by the cockpit computersystem.

DETAILED DESCRIPTION OF EMBODIMENT(S)

FIG. 1 is a plan view of an aircraft 10 showing its landing gears: anose landing gear (NLG) 1 and four main landing gears (MLGs) 2. FIG. 2shows a landing gear system for one of its four MLGs, comprising sixwheels, each wheel having a respective tire 3-8. Each wheel carries arespective sensor system 3 a-8 a for taking pressure and temperaturereadings from the wheel. All twenty two wheels of the aircraft haveequivalent sensor systems.

Each sensor system 3 a-8 a has a wireless transmitter for wirelesslytransmitting data to a receiver 12. The receiver 12 may either bemounted on a strut of the landing gear, or within a landing gear bayinto which the landing gear retracts after take-off. Alternatively eachsensor system 3 a-8 a may be wired to the receiver 12.

FIG. 3 is a schematic view of a system for checking the pressures of thetires of the aircraft 10. Only two of the sensor systems 3 a, 4 a areshown for purposes of clarity. Each sensor system comprises a pressuresensor 3 b, 4 b for measuring a pressure of the tire to generatepressure readings, and a temperature sensor 3 c, 4 c for measuring atemperature of the wheel to generate temperature readings. The receiver12 receives the pressure and temperature readings via connections whichmay be either wired or wireless and forwards the readings to a cockpitcomputer system 13 in the cockpit of the aircraft via a connection whichalso may be wired or wireless.

FIG. 4 is a schematic view of some of the elements of the cockpitcomputer system 13. The system comprises a receiver 20 for receiving thepressure and temperature readings from the receiver 12; a display device21; a memory 22; a processor 23; a user interface (UI) 24 such as atouch screen or keyboard; and a clock 25.

When the aircraft is on the ground before a flight, each sensor system 3a-8 a is operated to simultaneously record the temperature of itsassociated wheel and the pressure of its associated tire. The associatedground pressure and temperature readings are transmitted to the cockpitsystem 13 and stored in the memory 22. Each ground pressure reading isalso time-stamped based on a time reading from the clock 25.

Ground pressure readings are taken after a flight once the temperaturereadings are within 5° C. of ambient temperature (as measured by anambient temperature sensor—not shown). Ground pressure readings are alsotaken shortly before a flight. The ground pressure readings aredisplayed on the display device 21, along with associated warnings ifrequired.

Each ground pressure reading is also normalised based on its associatedtemperature reading and a common reference temperature of 15° C. toobtain a temperature-normalised ground pressure reading. This allows adirect comparison between pressure readings taken at differenttemperatures. The temperature-normalised ground pressure readings arecalculated by using the fact that a 10° C. temperature change changesthe tire pressure by approximately 3.7%. So for example if the groundpressure reading is 250 psi (pounds per square inch) and its associatedtemperature reading is 30° C., then the temperature-normalised groundpressure reading is calculated as:250−[250*(15/10)*0.037]=250−13.875=236.125 psi.

If there is insufficient time for the temperature readings to reduce towithin 5° C. of ambient temperature before the next flight, then groundpressure readings are taken 30 minutes after the last flight (at whichpoint the wheels will still be hot from braking). In this case theground pressure readings are adjusted to estimate the pressure atambient temperature. So for example if the ground pressure reading is240psi, its associated temperature reading is 50° C., and the ambienttemperature is 20° C., then the ambient-temperature-adjusted groundpressure reading is calculated as:240−[240*(30/10)*0.037]=240−26.64=213.36 psi.

This ambient-temperature-adjusted ground pressure reading is displayedon the display device 21, along with an associated warning if required.

At a later time, when the aircraft is in-flight, each sensor system 3a-8 a is operated again to simultaneously record the temperature of itsassociated wheel and the pressure of its associated tire. The in-flightpressure and temperature readings are transmitted to the cockpit system13 and stored in the memory 22 along with their time-stamps. When theaircraft is in the air, then the tires are unloaded so can be expectedto reduce in pressure by about 4%. Therefore the in-flight pressurereadings are not only normalised with respect to temperature, but alsoadjusted to take account of this unloading effect. So for example if theground pressure reading immediately before the flight is 250 psi, thein-flight pressure reading is 220 psi, and the in-flight temperaturereading is 10° C., then a temperature-normalised and load-adjustedin-flight pressure reading is calculated as:220+[220*(5/10)*0.037]+[250*0.04]=220 +4.07+10=234.07 psi.

Finally, at a later time when the aircraft is back on the ground after aflight, a further set of temperature-normalised ground pressure readingsare taken, one per tire, and recorded along with their time-stamps.

FIG. 5 is a graph showing a set of eight pressure readings. There arefour temperature-normalised ground pressure readings P_(g)(1)-P_(g)(4)and four temperature-normalised and load-adjusted in-flight pressurereadings P_(f)(1)-P_(f)(4). Between P_(g)(2) and P_(g)(3) the tire hasbeen inflated. The processor 23 fits a straight line 30 to the last fourpressure readings P_(g)(3), P_(f)(3), P_(f)(4), P_(g)(4) in order todetermine an estimated deflation rate. The estimated deflation rate iscalculated based on the last four pressure readings P_(g)(3), P_(f)(3),P_(f)(4), P_(g)(4), and the first four pressure readings P_(g)(1),P_(f)(1), P_(f)(2), P_(g)(2) are ignored since there has been a pressureincrease of more than 5 psi between P_(g)(2) and P_(g)(3). Since allfour of the pressure readings P_(g)(3), P_(f)(3), P_(f)(4), P_(g)(4)have been temperature-normalised to a common reference temperature of15° C., and load adjusted by 4% if required, then they can be validlycompared with each other to determine the deflation rate.

Any suitable method may be used to calculate the straight line 30—forinstance least-squares fitting. The gradient of the straight line 30gives an estimated deflation rate of R=ΔP/ΔT.

Estimated deflation rates are calculated for each tire. The processor 23determines the tire with the highest deflation rate, and optionallycompares the highest deflation rate with a threshold and provides awarning on the display device 21 if the estimated deflation rate exceedsa threshold. A suitable threshold may be for example a deflation ratewhich will result in a loss of pressure of more than 2% within 24 hours.So if the latest pressure reading is 250 psi, then a deflation rategreater than a threshold of (0.02*250)/24=0.208 psi/hr will result in awarning being displayed.

Table 1 below gives an example of a ground pressure reading of 250 psitaken with the wheel at a temperature of 20° C. The memory 22 stores areference pressure level of 244 psi, and the ground pressure reading iscompared with this reference pressure level to calculate a pressurepercentage. So for a ground pressure reading of 250 psi the pressurepercentage is 102%. Based on a deflation rate of 0.34 psi/hr, thepressure will reduce from 250 psi to the reference pressure level (244psi) in 6 hours and to 95% of the reference pressure level in 53 hours.Note that in this case, since the wheel is at a relatively lowtemperature, the time for the tire to deflate to 100% and 95% iscalculated starting from an initial pressure reading 250 psi, withoutfirst adjusting the initial pressure reading with respect totemperature. So in this case the time estimates of 6 hours and 53 hoursare based on the assumption that the temperature does not change from20° C.

TABLE 1 Pressure reading (psi) 250 Pressure percentage (%) 102Temperature (deg C.) 20 Deflation Rate (psi/hr) = 0.34 Pressuredifference to reach 100% 6 (244 psi) Time to deflate to 100% (hr) 18hours Pressure difference to reach 95% 18 (232 psi) Time to deflate to95% (hr) 53 2 days 5 hours

In the example of Table 1 the deflation rate of 0.34 psi/hr is greaterthan the threshold of (0.02*250)/24=0.208 psi/hr so a warning may bedisplayed in addition to the data presented in Table 1.

Table 2 below gives an example of a ground pressure reading of 300 psitaken with the wheel at a high temperature of 55° C. In this case,unlike in Table 1 above, the time for the tire to deflate to thereference pressure level is calculated by first reducing the pressurereading with respect to an ambient temperature reading (in this case 15°C.) taken by an ambient temperature sensor (not shown) to obtain atemperature-adjusted pressure level, and then calculating a time for thetire to deflate from this temperature-adjusted pressure level to thereference pressure level based on the estimated deflation rate. Thisgives a temperature-adjusted pressure reading of 256 psi (105%), andbased on a deflation rate of 0.34 psi/hr, the pressure will reduce from256 psi (105%) to the reference pressure level (244 psi) in 34 hours andto 95% of the reference pressure level in 69 hours. So in this case thetime estimates are based on the assumption that the temperature reducesfrom 55° C. to the lower ambient temperature of 15° C. Note that theambient temperature reading in this example is 15° C., which iscoincidentally the same as the common reference temperature mentionedabove used for calculating the estimated deflation rate. However thisneed not be the case, and the ambient temperature reading may instead be10° C. or 20° C. for example.

TABLE 2 Pressure reading (psi) 300 Pressure percentage (%) 123Temperature (deg C.) 55 Pressure Loss per hour (psi/hr) = 0.34 PressureAdjusted to ambient 15° C. (psi) 256 Pressure Adjusted to ambient 15° C.(%) 105 Pressure difference to reach 100% 12 (244 psi) Time to deflateto 100% (hr) 34 1 day 10 hours Pressure difference to reach 95% 24 (232psi) Time to deflate to 95% (hr) 69 2 days 21 hours

FIG. 6 is an example of a display screen which can be presented to theflight crew on the display 21. Note that this display screen is for adifferent aircraft with only six wheels rather than twenty two (as inthe example of FIG. 1). For each wheel, a tire pressure, pressurepercentage and temperature are displayed along with the estimated timeto reach 100% and 95%. The example of FIG. 6 presents the information inthe form of a table, but alternatively the information may be displayedgraphically.

The estimated time is based on the time stamp and actual pressure of themost recent pressure reading for each tire (rather than being based onthe current time or a temperature-adjusted pressure reading).

If the percentage is below 100% then a warning is displayed in thecolumn headed “TIRE PRESSURE WARNING”.

The ambient temperature sensor (not shown) measures the current ambienttemperature, which is displayed along with the name of the destinationairport and the destination temperature at the expected arrival time.This destination temperature can be obtained automatically by theprocessor 23 by means of a weather forecast for the destination, orcould be entered manually via the user interface 24.

Temperature-adjusted pressure readings are calculated based on thecurrent ambient temperature, and displayed in the column headed“ESTIMATE PRESSURE AT AMBIENT”. So for example if the ground pressurereading is 280 psi, its associated ground temperature reading is 50° C.,and the ambient temperature is 20° C., then the estimated pressure atambient is calculated as: 280−[280*(30/10)*0.037]=280−31.08=248.92 psi.

Temperature-adjusted pressure readings are also calculated based on theestimated destination temperature, and displayed in the column headed“ESTIMATE PRESSURE AT DESTINATION”. So for example if the groundpressure reading is 280 psi, its associated ground temperature readingis 50° C., and the destination temperature is 0° C., then the estimatedpressure at destination is calculated as:280−[280*(50/10)*0.037]=280−51.8=228.2 psi.

A low estimated pressure at the destination may generate a warning whichprompts ground crew to inflate the tire further before the flight.

The reference pressure levels for the wheels of the nose landing gearand the main landing gear (by which the pressure percentages arecalculated) are also displayed.

The method described above may be implemented by the cockpit system 13,in cooperation with the sensor systems 3 a-8 a, or it may be implementedby a hand-held device (not shown) which is used by ground crew tointerrogate the sensor systems 3 a-8 a and calculate and display theinformation shown in FIG. 6.

The tire pressure monitoring method described above is performed toprovide a history of the tire pressure for each wheel and to provideadvanced notification of impending problems and recommended actions:specifically it is possible to help predict when the next tire inflationwill be required; to detect the onset of failures by monitoring the rateof pressure loss for each wheel and detecting higher than averagedeflation rates; and to detect poor tire inflation practices.

In the embodiment of the invention described above, wheel temperaturesensors 3 c, 4 c are provided to generate wheel temperature readings foreach wheel. Brake temperature sensors (not shown) are also provided fortaking brake temperature readings for each wheel of the MLGs 2 (althoughthere are no brakes, and hence no brake temperature sensors, for the NLG1). If wheel temperature readings are not available (either if the wheeltemperature sensors 3 c, 4 c are not working, or not provided) then thesystem may use brake or ambient temperature readings as a substitute forthe wheel temperature readings by the following process. After a flight,ground pressure readings and associated brake and ambient temperaturereadings are taken once the brake temperature reading is the same as theambient temperature reading +/−5° C. (as read by the ambient temperaturesensor), or the brake temperature reading is equal to 5° C., or after 3hours since last flight and the brake temperature reading is less than50° C. For the MLGs 2 the ground pressure readings are normalised basedon their associated brake temperature readings, and for the NLG 1 theground pressure readings are normalised based on their associatedambient temperature readings.

If brake temperature readings are not available for a given tire thenits tire pressure can be recorded at the same time as the pressure ofits axle mate (i.e. the tire sharing the same axle). If the axle mate'stemperature is also not available then the tire pressure is recordedwhen the last tire pressure on that landing gear is recorded.

The tire pressure readings and ambient temperature readings for eachwheel of the NLG 1 are recorded when the readings for the MLGs 2 aretaken. If no MLG readings have been taken (due to a quick turnaround)then tire pressure readings and ambient temperature readings for eachwheel of the NLG 1 are recorded at engine start.

If the aircraft has been in flight for a long period of time, then whenthe processor 23 is notified that the landing gears are extending(indicating that the aircraft is coming in to land) this is used as atrigger to take in-flight pressure readings and associated braketemperature readings. This in-flight method only applies to the MLGs 2since brake temperature readings are not available for the NLG 1.

While at least one exemplary embodiment of the present invention(s) isdisclosed herein, it should be understood that modifications,substitutions and alternatives may be apparent to one of ordinary skillin the art and can be made without departing from the scope of thisdisclosure. This disclosure is intended to cover any adaptations orvariations of the exemplary embodiment(s). In addition, in thisdisclosure, the terms “comprise” or “comprising” do not exclude otherelements or steps, the terms “a” or one do not exclude a plural number,and the term “or” means either or both. Furthermore, characteristics orsteps which have been described may also be used in combination withother characteristics or steps and in any order unless the disclosure orcontext suggests otherwise. This disclosure hereby incorporates byreference the complete disclosure of any patent or application fromwhich it claims benefit or priority.

The invention is:
 1. A method of monitoring the pressure of a tire of anaircraft by a computer system, the method comprising: taking two or morepressure readings from the tire at different times; calculating anestimated deflation rate of the tire based on the two or more pressurereadings; comparing the estimated deflation rate with a threshold anddisplaying using a display device a warning if the estimated deflationrate exceeds the threshold; wherein at least one of the pressurereadings is an in-flight pressure reading with the tire unloaded, andthe other pressure reading is an on the ground pressure reading; and,wherein the ground pressure readings are taken between shortly before aflight and after a flight once the temperature readings are within 5° C.of ambient temperature.
 2. The method of claim 1 further comprisingcalculating a time for the tire to deflate to a reference pressure levelbased on the estimated deflation rate.
 3. The method of claim 2 furthercomprising displaying the time for the tire to deflate to the referencepressure level.
 4. The method of claim 1, further comprising calculatinga first time for the tire to deflate to a first reference pressure levelbased on the estimated deflation rate, and calculating a second time forthe tire to deflate to a second reference pressure level based on theestimated deflation rate.
 5. The method of claim 4 further comprisingsimultaneously displaying the first and second times on a single displaydevice.
 6. The method of claim 1 further comprising for each pressurereading taking an associated temperature reading, wherein the estimateddeflation rate is calculated by normalising each pressure reading basedon its associated temperature reading and a common reference temperatureto obtain a temperature-normalised pressure reading, and calculating theestimated deflation rate based on the temperature-normalised pressurereadings.
 7. The method of claim 1 wherein the estimated deflation rateis calculated by adjusting the in-flight pressure reading to takeaccount of the tire being unloaded to obtain a load-adjusted in-flightpressure reading, and calculating the estimated deflation rate based onthe load-adjusted in-flight pressure reading.
 8. The method of claim 6wherein the in-flight pressure reading is normalised based on itsassociated temperature reading and the common reference temperature andalso adjusted to take account of the tire being unloaded, to obtain atemperature-normalised and load-adjusted in-flight pressure reading, andthe estimated deflation rate is calculated based on thetemperature-normalised and load-adjusted in-flight pressure reading. 9.The method of claim 1, wherein the estimated deflation rate iscalculated based on three or more pressure readings taken from the tireat different times.
 10. The method of claim 1, wherein the estimateddeflation rate is calculated by a computer system.
 11. Apparatus formonitoring the pressure of a tire of an aircraft, the apparatuscomprising: a pressure sensor for taking pressure readings from the tireat different times; a computer system configured to calculate anestimated deflation rate based on two or more of the pressure readingsand compare the estimated deflation rate with a threshold to provide awarning if the estimated deflated rate exceeds the threshold; wherein atleast one of the pressure readings is an in-flight pressure reading withthe tire unloaded and the other pressure reading is an on the groundpressure reading; and, wherein the ground pressure reading are takenbetween shortly before a flight and after a flight once the temperaturereadings are within 5° C. of ambient temperature.
 12. The apparatus ofclaim 11 wherein the computer system is configured to estimate a timefor the tire to deflate to a reference pressure level based on theestimated deflation rate.
 13. The apparatus of claim 11, wherein thecomputer system is configured to compare the estimated deflation ratewith a threshold, and provide a warning if the estimated deflation rateexceeds the threshold.
 14. The apparatus of claim 11 further comprisinga temperature sensor for taking temperature readings, wherein theestimated deflation rate is calculated by normalising each pressurereading based on an associated temperature reading from the temperaturesensor and a common reference temperature to obtain atemperature-normalised pressure reading, and the computer system isconfigured to calculate the estimated deflation rate based on thetemperature-normalised pressure readings.
 15. A method to monitor a gastemperature in a tire of an aircraft by a computer system, the methodcomprises: measuring a pressure of a gas in the tire of the aircraft ateach of two or more different points in time; transmitting the measuredpressures to a computing device; calculating by the computing device arate of deflation of the tire based on the measured pressures and thepoints in time at which the measurements were performed; comparing theestimated deflation rate with a threshold and displaying using a displaydevice a warning if the estimated deflation rate exceeds the threshold;wherein at least one of the pressure readings is an in-flight pressurereading with the tire unloaded, and the other pressure reading is an onthe ground pressure reading; wherein the ground pressure readings aretaken between shortly before a flight and after a flight once thetemperature readings are within 5° C. of ambient temperature; and,displaying an alert on a display device associated with the computingdevice if the rate of deflation is greater than a threshold rate ofdeflation.
 16. The method of claim 15 further comprising: measuring atemperature of the gas in the tire at each of the two or more differentpoints of time; calculating by the computing device, for each of the twoor more different points of time, an adjusted pressure in the tire basedrepresenting a predicted gas pressure in the tire for the gas at areference temperature, wherein the reference temperature is used tocalculated the adjusted pressure for all of the two or more differentpoints of time, and the calculation of the rate of deflation isperformed using the adjusted pressures each corresponding to one of thetwo or more different points of time.
 17. The method of claim 15 whereinat least one of the different points in time corresponds to a timeduring which the aircraft is in flight and the tire is not supportingthe aircraft, and the method further comprises: calculating by thecomputing device an adjusted pressure based on the measured pressurecorresponding to the time during which the tire is not supporting theaircraft, wherein the adjusted pressure represents a predicted gaspressure in the tire if the tire where supporting the aircraft, and thecalculation of the rate of deflation is performed using the adjustedpressure for the time during which the tire is not supporting theaircraft.
 18. The method of claim 17 further comprising: measuring atemperature of the gas in the tire at each of the two or more differentpoints of time; calculating by the computing device, for each of the twoor more different points of time, an temperature adjusted pressure inthe tire based representing a predicted gas pressure in the tire for thegas at a reference temperature, wherein the reference temperature isused to calculated the temperature adjusted pressure for all of the twoor more different points of time, and the calculation of the rate ofdeflation is performed using the temperature adjusted pressures eachcorresponding to one of the two or more different points of time.